In this paper, a graph-theory-based approach for representing planar mechanisms is presented, the Santiago Portilla method (SPM). From the corresponding adjacency matrix, SPM generates an extended matrix containing the complete characterization of a planar mechanism, including all the information about both topology and geometry. This matrix representation can be used for the optimal design of mechanisms, allowing simultaneously the topological and dimensional synthesis by means of computational tools such as the metaheuristic algorithms. A case study corresponding to the design of a fixed-linear-trajectory tracker mechanism is included in order to test the efficiency of the proposed approach. It was carried out by addressing the design as an optimization problem and solving it with the differential evolution algorithm, representing the individuals in its population by the matrix form generated by the SPM. The results of the case study show that the SPM and its matrix representation constitute a useful and flexible tool for the solution of the real engineering problems involving the design of planar mechanisms.
